ABSTRACT

This chapter begins with a basic review of probability and statistics and develops the mathematical tools for seismic performance assessment and design. Probability may be considered as a tool for carrying defined uncertainty through the components of an engineering problem—it starts where classic, deterministic, engineering models end. The concept of conditional probability provides the necessary formalism to define what is meant by independence. In parallel to the normal distribution, the lognormal distribution is the model for the product of independent random variables, and it possesses a large number of interesting mathematical properties that are discussed in detail in any good probability book. The chapter provides the tools for assessing whether a structure meets or violates performance objectives by employing the results of multiple nonlinear response history analyses. Performance-based seismic design means setting any number of performance objectives, and applying a method that can produce a structural solution to satisfy them within the applicable constraints.